Problem: Multiply the following complex numbers: $({-5+i}) \cdot ({3-2i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5+i}) \cdot ({3-2i}) = $ $ ({-5} \cdot {3}) + ({-5} \cdot {-2}i) + ({1}i \cdot {3}) + ({1}i \cdot {-2}i) $ Then simplify the terms: $ (-15) + (10i) + (3i) + (-2 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -15 + (10 + 3)i - 2i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -15 + (10 + 3)i - (-2) $ The result is simplified: $ (-15 + 2) + (13i) = -13+13i $